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  • The ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is : &nb

The ordinary dice is rolled for a certain number of times. If the probability of getting an odd number 2 times is equal to the probability of getting an even number 3 times, then the probability of getting an odd number for odd number of times is :  
Option: 1 \frac{3}{16}
Option: 2 \frac{1}{32}
Option: 3 \frac{5}{16}
Option: 4 \frac{1}{2}

Answers (1)

best_answer

 

\\\mathrm{P}(\text { odd no. twice })=\mathrm{P}(\text { even no. thrice }) \\ \\\Rightarrow{ }^{n} \mathrm{C}_{2}\left(\frac{1}{2}\right)^{\mathrm{n}}={ }^{n} \mathrm{C}_{3}\left(\frac{1}{2}\right)^{\mathrm{n}} \Rightarrow \mathrm{n}=5

\begin{aligned} &\text { success is getting an odd number then } \mathrm{P}(\text { odd successes })=\mathrm{P}(1)+\mathrm{P}(3)+\mathrm{P}(5)\\ &={ }^{5} C_{1}\left(\frac{1}{2}\right)^{5}+{ }^{5} C_{3}\left(\frac{1}{2}\right)^{5}+{ }^{5} C_{5}\left(\frac{1}{2}\right)^{5}\\ &=\frac{16}{2^{5}}=\frac{1}{2} \end{aligned}

Posted by

Suraj Bhandari

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